The Role of Semantic Understanding in Solving Multiplication & Division Word Problems. Final Report.

Schwartz, Judah L.

The learning of word problems in mathematics is viewed as particularly difficult. The first paper in this report takes into consideration the semantic aspects of problems, by viewing the difficulties that children have solving two-step multiplication problems. An initial study was carried out with 36 children between the ages of nine and fourteen years old; a subsequent experiment involved 93 pupils between the ages of nine and thirteen years. Among the results, the investigations indicated that the concept of ratio was a major source of difficulty in solving problems. Also, being a two-step problem to begin with was a major source of difficulty. It was felt that further study of these two issues could allow for design of teaching strategies to help children surmount these difficulties. The second paper in this document focuses further on the child's development of ratio concepts, with 36 children between the ages of ten and thirteen participating. The results of this investigation served to confirm prior findings that the notion of ratio as a quantity is difficult for children. (MP)